Essays on Economic Theory and Applications

The first chapter studies global games with interim information acquisition, where players acquire additional information about signal precision after they observe private signals. In the first period, players receive private signals with unknown precision and then choose costly efforts to investigate the precision of the signal. In the second period, players play a global game conditional on their signals and investigation results. We first provide sufficient conditions on the two key parameters---the precision of the public signal and the precision of the private signal---under which the game has a unique equilibrium. The optimal information acquisition decision as a function of private signals is then characterized. Relative to the case in which there is no uncertainty on information qualities, this additional information friction increases the likelihood of regime change when the regime is strong and decreases the likelihood when the regime is weak. We also analyze how players with different private information would react to changes in public information. Finally, it is shown that information decisions may not always exhibit strategic complementarities even in a game with strategic complementarities in actions. Our results shed lights on how social media affect collective actions\u27 such as financial crisis, bank runs and strategic entry deterrence. The second chapter studies how interim information acquisition affects social welfare. Investors collect information from various sources before they make investment decisions. To identify and explore the trustworthy of the information source requires extra time and effort. Do investor really benefit from acquiring additional information? To answer the question we study a beauty contest game with information acquisition. On the one hand, additional information helps investors to estimate the underlying state more accurately, while on the other hand it could create disagreement among investors and decrease the social welfare through dispersed actions. The impact on social welfare therefore depends on these two conflicting effects. We show that in a game with strategic complementarities the first effect dominates, so acquiring more information about the quality of signals always enhance social welfare. In the third chapter, we study two person infinitely repeated games in which players move alternately. Players choose finite state automata instead of actions at each stage and at the end of each period there is a chance for each player to be committed to the prevailing automaton. We analyze the subgame perfect equilibrium in this asynchronously repeated automaton game with commitment. The main result shows that the well-known folk theorem does not hold under our constructions and a stronger prediction about the equilibrium payoff set is induced. In particular, in the repeated battle of sexes game, provided that a small enough probability of commitment is fixed, the equilibrium payoff vector will be located in a small neighborhood of the symmetric Pareto efficient payoff vector as the players become sufficiently patient. In the final chapter, we introduce a new solution concept called M-rationalizability. The electronic mail game introduced by Rubinstein (1989) shows that a lack of common knowledge can lead to a different prediction of the rationalizable strategies from that with common knowledge. This paper tries to bridge the discrepancy by introducing a new type of players into Baysian games with countable type spaces. The new type of players, called mutant type in the context, may make mistakes stochastically when he deduce the rationalizable actions of each type of other players. In particular, it is shown that in the email game, no matter how small the probability of making a mistake is, the set of rationalizable strategies is the same as that in the game when we have common knowledge if the number of messages is sufficiently large